Demand response has been widely utilized to provide frequency regulation service for the power systems by adjusting the power consumption of flexible loads. The frequency regulation service is time-sensitive and generally realized by direct load control, due to the quick response requirement (generally a few seconds). Most of the existing studies assume that the control on flexible loads can be implemented immediately without communication latency (CML), and the system frequency deviations can be detected without errors (FDE). However, in reality, the CML and FDE are ever-present during the control process and can influence the effectiveness of regulation significantly. To address this issue, this paper develops the aggregation models of ON-OFF flexible loads and continuously adjustable flexible loads, respectively. The centralized and distributed control methods considering the CML and FDE are developed, respectively. On this basis, a novel hybrid control method is proposed to compensate the CML and FDE, in which the modification method is developed for improving the estimation accuracy of the FDE. The results in the numerical studies show that the maximum system frequency deviation extends from -0.112 Hz to -0.120 Hz and -0.221 Hz due to the FDE and CML, respectively. After the modification by the proposed hybrid control method, the maximum frequency deviation is decreased to -0.110 Hz, which is almost equal to the ideal value when there is no FDE and CML. Therefore, this research can compensate the CML and FDE well, which is useful for guiding demand response projects in smart grid.